(x+4)(x+1)=28

Solution for (x+4)(x+1)=28 equation:

Simplifying
(x + 4)(x + 1) = 28

Reorder the terms:
(4 + x)(x + 1) = 28

Reorder the terms:
(4 + x)(1 + x) = 28

Multiply (4 + x) * (1 + x)
(4(1 + x) + x(1 + x)) = 28
((1 * 4 + x * 4) + x(1 + x)) = 28
((4 + 4x) + x(1 + x)) = 28
(4 + 4x + (1 * x + x * x)) = 28
(4 + 4x + (1x + x2)) = 28

Combine like terms: 4x + 1x = 5x
(4 + 5x + x2) = 28

Solving
4 + 5x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
4 + -28 + 5x + x2 = 28 + -28

Combine like terms: 4 + -28 = -24
-24 + 5x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-24 + 5x + x2 = 0

Factor a trinomial.
(-8 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-8, 3}